Pat chicken dry. Season chicken all over with 2 teaspoons of the salt and 1/4 teaspoon of the pepper.
In a large Dutch oven or similar large, sturdy pot melt 2 tablespoons butter over medium high. Add half of the chicken pieces in a single layer, skin side down—make sure the chicken isn’t crowed or it won’t brown properly. Let sear without disturbing until the skin is golden brown, about 4 minutes. Remove to a plate (no need to sear the other side). Repeat with the remaining pieces.
Add 1 tablespoon butter to the pot, then add the mushrooms. Sauté until the mushrooms soften and brown, 5 to 6 minutes. Remove to a separate plate or bowl.
To the pot, add 1 tablespoon butter, the carrots, celery, yellow onion, and remaining 1/2 teaspoon salt and 1/4 teaspoon black pepper. Reduce the heat to medium. Sauté until the vegetables are tender, about 6 minutes.
Sprinkle the flour over the top. Cook, stirring constantly, until the flour turns golden, about 1 full minute.
Slowly pour in the wine, then use a wooden spoon to scrape up any browned bits on the bottom of the pot. Let cook and reduce for 2 minutes, stirring often. Add the chicken broth, stirring until smoothly combined.
Add the pearl onions, thyme bundle, bayleaf, and seared chicken along with any juices that have collected on the plate. The chicken should be just submerged in liquid; if it’s not, add more broth or water until it is. Bring the mixture to a simmer, then reduce the heat to low and cover. Cook the chicken, maintaining a very gentle simmer, for 30 minutes.
Remove the lid from the pot. Fish out the thyme bundle and bayleaf and discard. In a bowl or liquid measuring cup, whisk together the half-and-half and cornstarch, until smoothly combined. Add to the pot and stir. Stir in the nutmeg.
Increase the heat to bring the liquid to a simmer. Partially cover the pot and let simmer 10 minutes more. Periodically lift the lid and stir the pot, running a wooden spoon along the bottom to prevent sticking. The mixture will thicken slightly.
Stir in the lemon juice, parsley, and reserved mushrooms. Carefully taste and adjust the seasoning as desired. Serve hot over rice or mashed potatoes.
Notes
TO STORE: Refrigerate chicken fricassée in an airtight container for up to 3 days.
TO REHEAT: Warm up leftover chicken fricassée in a skillet on the stovetop over medium-low heat or in the microwave.
TO FREEZE: Freeze in an airtight, freezer-safe storage container for up to 3 months. Thaw overnight in the refrigerator before reheating according to the instructions above.